Heat 2 teaspoons of the butter in a skillet with a cover over medium heat. When the butter has melted, add the mushrooms and sauté for about 8 minutes. The mushrooms will soften and probably release some liquid as they cook. Continue cooking until all of the liquid has been released and evaporated, and the mushrooms start to brown a bit. Add the minced garlic and stir for 30 seconds. Add the spinach, season with salt and pepper, and sauté for two minutes until the spinach has wilted. Turn the vegetables onto a plate and set aside.
Wipe out the skillet, then return it to medium heat and add a half teaspoon of butter. Place a tortilla in the pan and cook for 30 seconds, then flip the tortilla. Sprinkle 2 tablespoons of the cheese mixture over half of the quesadilla, and distribute about 1/8 (a couple of tablespoons) of both the sautéed vegetable mixture and the shredded chicken over the cheese. Top that with another 2 tablespoons of the shredded cheese. Flip the bare half of the tortilla over the filling, cover the pan, and sauté for about 2 minutes until the bottom is golden and the cheese has started to melt, then use a spatula to flip the half-moon quesadilla and continue to cook, uncovered, until all of the cheese is melted and the underside is browned, 2 to 3 minutes.
Remove the quesadilla to a cutting board and let the quesadilla sit for a minute before you slice into 2 or 3 wedges. Repeat until all of the quesadillas are cooked. Serve with salsa and sour cream.
Notes
If you have leftover simply cooked chicken, use it here. You can use cooked dark meat or chicken breasts, whatever you prefer, whatever you have. If not, this is what rotisserie chickens were made for.
The olives are optional, but my kids love them. Use whatever mushrooms you like, from easy-to-find, inexpensive button or cremini mushrooms to any wild mushrooms you feel like including. And if mushrooms are not your family’s thing, leave those out, and then you have a chicken and spinach quesadilla (or leave out the spinach — and then you get chicken and mushroom quesadillas.
When you sauté the mushrooms and spinach, keep cooking them until any liquid that has been released evaporates in the pan. This will prevent the quesadillas from getting soggy.